The latter part of this claim seems strange in the light of the article itself. There is no discussion of sexism and little about gender or sex in the text. Falk only mentions that someone else had accused Asperger of sexism, and points out how Asperger influenced Simon Baron-Cohen and some other researchers:
Asperger’s comment that “the autistic personality is an extreme variant of male intelligence” (Asperger 1944b, p.84) anticipated Baron-Cohen’s “extreme male brain” theory (Baron-Cohen 2002). In addition to discovering that AS is recognized more frequently in boys than girls, Asperger hypothesized that this phenomenon may be associated with genetic as well as environmental factors: “There is certainly a strong hint as a sex-linked or at least sex-limited mode of inheritance” (Asperger 1944b, p.84). Although the topic of sex differences in autism is controversial (e.g., researchers differ in the extent to which they think camouflaging impacts apparent prevalence rates in females), contemporary researchers are fruitfully exploring this ‘hint’ (Beacher et al. 2012; Iossifov et al. 2015; Lai et al. 2011).Over the past years, I have occasionally tried to point out that Asperger's ideas about sex differences were probably typical of his era and cultural environment, but by modern standards they were deeply flawed. I believe that the flaws have been perpetuated in autism research and the shaping of diagnostic criteria. Further, I believe that this is one of the reasons behind autistic girls and women being under-identified and their needs not receiving proper consideration when services are planned and provided. This is not a small matter.
What were Hans Asperger's beliefs and attitudes concerning women? How have they guided the formation of current ideas and research directions? The following excerpts shed some light on what Asperger thought. They are from a second edition of Heilpädagogik, a textbook he wrote, published in 1956, at a time when he had had plenty of time to crystallize what was essential to his theory and approach. These were some of the things he wanted to pass on to students as the core of his knowledge regarding autism. I feel there is no reason to vilify him, but neither should we naively place him on a pedestal or attribute ideas or ideals to him that arose after his era. He made some very intelligent observations, and was right about many things concerning autism. He was utterly wrong about some things, blinded by common misconceptions. That is how most scientists are, if we look at them up close.
The translations are mine. Sorry about minor inaccuracies.They do not change the overall message.
"Looking at our autistic children in terms of their gender, we are faced with the astonishing fact that they are almost all boys. In girls, we did find contact disturbances, which in some cases resembled the autistic disorder; we found clinical pictures similar to schizophrenia, as well as girls in whom encephalitis was the cause of such a condition, but in our own material we did not find a single fully developed case of what we have described in this text. Is it a sex-linked hereditary condition, or at least limited to one sex? It is something akin to that.
The autistic mental disorder is an extreme variant of the male character, of male intelligence. Even within the normal range of variation, typical differences in intelligence exist between boys and girls: girls are generally better learners, suited to the concrete, the intuitive, the practical, and to working neatly and eagerly while following models provided for them, whereas boys are more logical, having the capacity for abstract thought, precise thinking and formulation, and independent research; when girls are capable of the latter, as well, they are usually types that lean towards the masculine."
(Hans Asperger, 1956, in Heilpädagogik, Zweite Auflage, p. 186)
"In autistic disorder, this behavior is emphasized to an extreme degree. Abstraction, which is more in the nature of masculine thinking, has advanced so far that its connections to the concrete, to things and to human beings, are very limited; adaptation to the demands of the environment, which still predominantly happens through instinctive functions, is achieved only to a very limited extent.
We find one observation that we were able to make in America very illuminating and typical: there are not only far greater numbers of autistic women, but an identical, in all details characteristic clinical picture is found in girls, not much less commonly than in boys. It appears to us that this fits well with another fact that often catches our attention there in other contexts, as well: in the US, the development of modern civilization is much more advanced than here, with hypertrophy of intellect and a gradual diminishing of instinctive functions, or a loss of integration between those two spheres of life, with the same threatening to happen here. This is particularly evident in the alteration of the female psyche (of course, this is especially obvious in the living conditions of the big city), in the sense of women's masculinization, which is reflected in numerous details of American public life. Intellectualization and loss of instinct, of course, are particularly noticeable in women, because the strength of the female psyche has until now relied above all on her being very different from man in her instinct, in her genuine emotion, in which men can never match her. Is it any wonder then that this development, brought on by women’s ”equal rights”, pushed through in America to a far greater extent than here, brings with it more frequent and intense occurrence of the "masculine forms of mental disorder" in such a population?"
(Hans Asperger, 1956, in Heilpädagogik, Zweite Auflage, p. 186-187)
I think we have to conclude that by any current standards of the western world Hans Asperger was definitely sexist. He did not only believe in the ideas expressed above, he taught them. He was not sexist solely because of being unaware of other ways of thinking. As the texbook shows, by the 1950s he had heard about equal rights, had dismissed the idea, and actively promoted the view that insisting on equality would distort girls' development and turn them into unnatural, masculine women. It looks like even many of his contemporaries might have had reason to consider him sexist. There is a tone in his writing which seems almost like he desperately wanted to defend his old-fashioned ideas from the onslaught of modernity, and that he might have allowed this emotional and ideological drive to influence how he formulated his understanding of autism. Current autism research or theory should not be built on this foundation. We need to pick what is real and usable, and finally, permanently discard the parts of Asperger's legacy that are complete nonsense.